Hindawi Publishing Corporation
Abstract and Applied Analysis
Volume 2012, Article ID 894769, 2 pages
doi:10.1155/2012/894769
Editorial
Variational Methods and Critical Point Theory
M. Victoria Otero-Espinar,1 Juan J. Nieto,1
Donal O’Regan,2 and Kanishka Perera3
1
Departamento de Análise Matemática, Facultade de Matemáticas, University of Santiago de Compostela,
15782 Santiago de Compostela, Spain
2
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland,
Galway, Ireland
3
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
Correspondence should be addressed to M. Victoria Otero-Espinar, mvictoria.otero@usc.es
Received 8 November 2012; Accepted 8 November 2012
Copyright q 2012 M. Victoria Otero-Espinar et al. This is an open access article distributed under
the Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Many applied problems can be understood and solved in terms of the minimization of a
functional, usually related to the energy, in an appropriate functional space. Minimization
and variational problems are at the interface between nonlinear analysis, calculus of
variations, differential equations, and mathematical physics and play a fundamental role in
the application of mathematics to real-world problems.
This special issue places its emphasis on the study and applications of variational
methods and critical point theory. The editors aim for this volume was first for it to serve
as a reference in the topic and second for it to collect several papers by specialists in the
area and from many different countries Algeria, China, Colombia, Czech Republic, France,
Greece, Iran, Italy, Japan, Malaysia, Poland, Romania, Saudi Arabia, Spain, and Thailand.
It includes several papers on different aspects such as nonlinear elliptic equations as
an example, in the work of M. Tanaka and L. Toscano and S. Toscano, the characterization
of the set of eigenvalues of nonlinear problems as an example, in the work of P. Drábek,
constrained variational equations as an example, in the work of M. Ruiz Galán, estimation
of the global attractor for evolution equations as an example, in the work of R. Colucci and
G. R. Chacón, existence of homoclinic orbits as an example, in the work of X. He, impulsive
problems as an example, in the work of H.-R. Sun et al., and fractional systems as an
example, in the work of J. Chen and X. H. Tang. It also contains applications to viscous
flow as an example, in the work of R. Fares et al., non-Newtonian filtration as an example,
in the work of X. Li et al., or oligopolistic market equilibrium as an example, in the work of
A. Barbagallo and P. Mauro.
Evidently, it is not possible to adequately represent in this special issue all directions
of current research in variational methods and critical point theory, but we believe that it
2
Abstract and Applied Analysis
reflects many important recent trends in research, indicates current challenging problems,
and outlines new ideas and open problems for future studies.
The guest editors of this special issue would like to express their gratitude to the
authors who have submitted papers for consideration. Thanks also to the many individuals
who served as referees of the submitted papers. All the participants have made it possible to
have a very stimulating interchange of ideas. We hope that these topics will stimulate future
research.
We would also like to thank the editorial board members of this journal, for their
support and help throughout the preparation of this special issue.
M. Victoria Otero-Espinar
Juan J. Nieto
Donal O’Regan
Kanishka Perera
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